Hokkaido Mathematical Journal

No. 2

MORI, Akira;

Nef Cone of a Generalized Kummer 4-fold.

Hokkaido Mathematical Journal, 50 (2021) pp.151-163

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In this note, we calculate the boundary of movable cones and nef cones of the generalized Kummer 4-fold $\mathrm{Km}^2(A)$ attached to an abelian surface $A$ with $\mathrm{rk} \mathrm{NS}(A) = 1$.

MSC(Primary)	14J35;
MSC(Secondary)
Uncontrolled Keywords	Generalized Kummer 4-fold; Nef cone; movable cone;

MICHIHISA, Hironori;

Optimal leading term of solutions to wave equations with strong damping terms.

Hokkaido Mathematical Journal, 50 (2021) pp.165-186

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We analyze the asymptotic behavior of solutions to wave equations with strong damping terms in $\textbf{R}^n$ $(n\ge1)$, $$ u_{tt}-\Delta u-\Delta u_t=0, \qquad u(0,x)=u_0(x), \quad u_t(0,x)=u_1(x). $$ If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the Fourier space are obtained, which implies the optimality of expanding methods and some estimates proposed in [13] and in this paper.

MSC(Primary)	35B40;
MSC(Secondary)	35L25; 35L30;
Uncontrolled Keywords	Strongly damped wave equation; Asymptotic expansion; Lower bound; Moment condition;

SEGATA, Jun-ichi;

Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension.

Hokkaido Mathematical Journal, 50 (2021) pp.187-205

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We consider the long time behavior of solutions to the initial value problem for the ``complex-valued'' cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the $L^{\infty}$ decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).

MSC(Primary)	35L71;
MSC(Secondary)	35B40;81Q05;
Uncontrolled Keywords	nonlinear Klein-Gordon equation; scattering problem;

REN, Guoqiang; LIU, Bin;

Boundedness of solutions for a quasilinear chemotaxis-haptotaxis model.

Hokkaido Mathematical Journal, 50 (2021) pp.207-245

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In this paper, we deal with the chemotaxis-haptotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded convex domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by $L^p$-estimate techniques, we show that the system possesses at least one global and bounded weak solution. Our results generalize and improve previous results.

MSC(Primary)	35D30;
MSC(Secondary)	35K45;35A01;35Q92;92C17;
Uncontrolled Keywords	Chemotaxis-haptotaxis; Boundedness; Global existence;

OCHI, Ryo;

A remark on the freeness condition of Suzuki's correspondence theorem for intermediate C$^*$-algebras.

Hokkaido Mathematical Journal, 50 (2021) pp.247-262

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Let $\Gamma$ be a discrete group satisfying the approximation property (AP). Let $X$, $Y$ be $\Gamma$-spaces and $\pi \colon Y \to X$ be a proper factor map which is injective on the non-free part. We prove the one-to-one correspondence between intermediate C$^*$-algebras of $C_0(X) \rtimes_r \Gamma \subset C_0(Y) \rtimes_r \Gamma$ and intermediate $\Gamma$-${\rm C}^\ast$-algebras of $C_0(X) \subset C_0(Y)$. This is a generalization of Suzuki's theorem that proves the statement for free actions.

MSC(Primary)	46L05;
MSC(Secondary)	37B05;
Uncontrolled Keywords	Intermediate C$^*$-subalgebras;